System and method for inductance based position encoding sensorless SRM drives

ABSTRACT

A controller ( 72 ) for a switched reluctance machine ( 20 ) implements a model of at least one active phase representing dynamic magnetic machine characteristics. The controller ( 72 ) determines machine control signals based on rotational position obtained by numerically solving the model with measured machine operating parameters. The model may be implemented as the sum of orthogonal functions relating active phase voltage and current with constants derived from phase inductance to obtain the rotor angle.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. §119 of PCT applicationnumber PCT/US01/09986, filed Mar. 29, 2002, entitled “System and Methodfor Inductance Based Position Encoding Sensorless SRM Drives” whichclaims priority to provisional application No. 60/193,012 filled Mar.29, 2000.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates generally to Switched Reluctance Machines (SRMs)and, more particularly, to a system and method for inductance basedposition encoding for sensorless SRM drives.

2. Background Art

Switched reluctance machine (SRM) drives have been considered as apossible alternative to conventional drives in several variable speeddrive applications because of the many advantages associated with SRMsystems. The performance of an SRM drive can be tailored to suit severalapplications through appropriate control. Other advantages includeconstructional simplicity of the machine such as, for example, theabsence of permanent magnets and windings in the rotor; fault tolerantoperation of the inverter; an extended high speed operating range; andthe like. Recent literature indicates that SRM drives are suitable forelectric vehicles, electric traction applications, home appliances,consumer applications, automotive applications, power steeringapplication in vehicles, aircraft starter/generator systems, and thelike.

Rotor position sensing is an integral part of SRM control due to thenature of torque production. Sensorless control reduces overall cost anddimension of the drive in addition to improving reliability. Also, thereare certain applications, such as in compressors, where the ambientconditions do not allow the usage of external position sensors.

A switched reluctance machine, whether functioning as a motor or agenerator, is basically a doubly salient, singly-excited machine thatoperates on the basis of a reluctance torque generation principle. Eachstator phase is excited with pulses of active currents during thepositive inductance slope region in order to develop positiveunidirectional torque. This requires synchronization of the stator phaseexcitation with rotor position. Usually, external mechanical positionsensors such as resolvers or optical encoders are used. However, thesesensors are expensive and experience reliability problems. Varioussensorless techniques have been published in the literature which mainlyuse terminal measurements or diagnostic signals to infer the rotorposition.

Several sensorless control methods have been reported. These methods canbe broadly classified as signal injection methods, state observermethods, flux integration methods, signal power measurement methods, andthe like. Each of the various methods suggested have merits and demeritsdepending on the principles of operation. Ideally, a sensorless schemewhich uses only terminal measurements and does not require additionalhardware is preferred.

SUMMARY OF THE INVENTION

Accordingly, an improved system and method for achieving sensorlesscontrol of SRM drives is needed. To fulfill this need, a system andmethod of achieving sensorless control of SRM drives using only activephase voltage and current measurements is provided. The sensorlesssystem and method generally relies on the dynamic model of the SRMdrive. Active phase currents are measured in real-time and, using thesemeasurements, the dynamic equations representing the active phases aresolved through numerical techniques to obtain rotor positioninformation. The phase inductances are represented by a Fourier serieswith coefficients expressed as polynomial functions of phase currents tocompensate for magnetic saturation. The controller basically runs theobserver in parallel with the drive system. Since the magneticcharacteristics of the motor are accurately represented, the statevariables, as computed by the observer, are expected to match the actualstate variables. Thus rotor position, which is also a state variable,will be available indirectly.

A method of controlling a multiphase switched reluctance machine isprovided. The method includes measuring the self-inductance of eachphase at a plurality of points in a phase rotation. A mathematical modelof inductance for each phase is constructed based on the measuredpoints. The mathematical model relates phase voltage to phase rotationangle through phase self-inductance. The phase current of eachconducting phase of the machine is measured while the machine is inoperation. The phase rotation angle is determined based on the measuredphase current and the mathematical model. The machine is controlledbased on the determined phase rotation angle.

In an embodiment of the present invention, the mathematical modelcomprises a sum of orthogonal functions. The mathematical model may beimplemented as a truncated Fourier series expansion.

In another embodiment of the present invention, measuring theself-inductance of each phase comprises measuring phase self-inductanceat an aligned position and measuring phase self-inductance at anunaligned position. Measuring the self-inductance may further includemeasuring phase self-inductance at at least one position between thealigned position and the unaligned position.

A method of measuring the rotational position of a switched reluctancemachine rotor is also provided. A mathematical model is generated basedon inductance values measured for each of at least one excited phase.The mathematical model relates at least one machine parameter with rotorrotational position. The one or more machine parameters are measuredduring machine operation. The machine rotational position is determinedby solving the mathematical model with the measured machine parameters.

In an embodiment of the present invention, the at least one measurablerotor parameter comprises at least one phase self-inductance.

In another embodiment of the present invention, the mathematical modelincludes a sum of orthogonal functions.

A switched reluctance system is also provided. The system includes aswitched reluctance machine having a rotor and a plurality of statorphases. A drive switches each stator phase current. A controllersupplies control signals to the drive. The controller receives at leastone sensed machine parameter from the switched reluctance machine. Thecontroller generates control signals based on a rotor positiondetermined from the sensed machine parameter and from a mathematicalmodel based on inductance values measured for at least one of the statorphases, the mathematical model relating the sensed machine parameterwith rotor position.

A method of controlling a switched reluctance machine is also provided.At least one active phase of the switched reluctance machine is modeledto produce a model representing dynamic magnetic machinecharacteristics. At least one of active voltage and current of the atleast one active phase is measured and the model solved to obtain rotorposition. Machine control signals are determined based on the rotorposition.

A controller for a switched reluctance machine is also provided. Thecontroller implements a model of at least one active phase of theswitched reluctance machine representing dynamic magnetic machinecharacteristics. The controller determines machine control signals basedon rotor position obtained by numerically solving the model with atleast one of measured active phase voltage and current.

The above objects and other objects, features, and advantages of thepresent invention are readily apparent from the following detaileddescription of the best mode for carrying out the invention when takenin connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram of a cross-sectional view of a three-phase switchedreluctance machine;

FIG. 2 is a diagram of idealized inductance, current and torquewaveforms during motoring/generating operations;

FIG. 3 is a block diagram illustrating an SRM system according to anembodiment of the present invention;

FIGS. 4 a–4 c are schematic diagrams illustrating aligned rotor, midwayaligned rotor and unaligned rotor positions, respectively;

FIGS. 5 a–5 b are graphs illustrating simulated actual and estimatedrotor angles, respectively, for a slowly rotating SRM according to anembodiment of the present invention;

FIGS. 6 a–6 b are graphs illustrating simulated phase currents andestimated rotor angles, respectively, for a slowly rotating SRMaccording to an embodiment of the present invention;

FIGS. 7 a–7 b are graphs illustrating simulated actual and estimatedrotor angles, respectively, for a rapidly rotating SRM according to anembodiment of the present invention;

FIGS. 8 a–8 b are graphs illustrating simulated phase current andestimated rotor angles, respectively, for a rapidly rotating SRMaccording to an embodiment of the present invention;

FIGS. 9 a–9 b are graphs illustrating simulated phase current andestimated rotor angles, respectively, for an SRM with overlapping phasecurrents according to an embodiment of the present invention;

FIGS. 10 a–10 b are graphs illustrating simulated rotor speed andestimated rotor angle, respectively, for an SRM undergoing transientchanges in rotational velocity according to an embodiment of the presentinvention; and

FIG. 11 is a flow diagram of controller operation according to anembodiment of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT(S)

Referring to FIG. 1, a diagram of a cross-sectional view of athree-phase switched reluctance machine is shown. A switched reluctancemachine (SRM), shown generally by 20, includes stator 22 and rotor 24which turns within stator 22. Stator 22 includes a plurality of statorphases, one of which is labeled 26. Each stator phase is driven bystator windings 28, shown cross-hatched. Rotor 24 includes a pluralityof poles, one of which is indicated by 30. SRM 20, in the example shown,has six phases 26 and four poles 30. Typically, opposing phases 26 aresimultaneously supplied with phase current. SRM 20 is, therefore,considered to be a three-phase machine. Opposing phases 26 may beconveniently labeled with the same letter. Phases 26 in SRM 20 arelabeled A, A′, B, B′, C and C′. Poles 30 in SRM 20 are labeled a, b, cand d.

Referring now to FIG. 2, a diagram of idealized inductance, current andtorque waveforms during motoring/generating operations is shown. Plot 40illustrates inductance for one phase 26 as a function of the position ofrotor 24. As pole 30 rotates past phase 26, the inductance of phase 26increases to a maximum when pole 30 is aligned with phase 26. Theinductance of phase 26 then decreases until pole 30 is unaligned withphase 26. When SRM 20 is motoring, phase current is applied to phase 26as rotor 30 rotates into alignment with phase 26, as illustrated by plot42, generating torque as illustrated by plot 44. When SRM 20 isgenerating, torque is applied, as illustrated by plot 46, generatingphase current as illustrated by plot 48.

Referring now to FIG. 3, a block diagram illustrating an SRM systemaccording to an embodiment of the present invention is shown. An SRMsystem, shown generally by 60, includes SRM 20. SRM 20 has shaft 62rotatively coupled to rotor 30. Shaft 62 provides a means to outputtorque when SRM 20 is functioning as a motor and provides a means toinput torque when SRM 20 is functioning as a generator. Phase lines 64conduct electrical power between each phase 26 and drive 66. When SRM 20is functioning as a motor, drive 66 switches electrical power from line68 onto each phase line 64 based on control signals 70 received fromcontroller 72. When SRM 20 is functioning as a generator, line 68supplies electrical power on line 68 by switching power received fromeach phase line 64 based on control signals 70 received from controller72.

Controller 72 receives as inputs at least one sensed operating parameterfrom SRM 20. This may include one or more of phase voltages and phasecurrents as measured by sensors 74. An advantage of the presentinvention is that the position of rotor 24 need not be explicitlymeasured. Controller 72 generates control signals 70 based on theposition of rotor 24 determined from the at least one sensed machineparameter and from a mathematical model based on inductance valuesmeasured for at least one of stator phases 26. The mathematical modelrelates the at least one sensed machine parameter with the position ofrotor 24.

The dynamics of SRM system 60 can be represented by a set of non-linearfirst-order differential equations which can be solved to obtain theperformance. Model input includes the excitation pattern, controlstrategy and rotor position information. Model output includes the phasecurrents, torques and other mechanical quantities. Model accuracydepends on the accuracy of inductance terms in the voltage equations,which are basically static characteristics of the motor, and onmechanical constants such as inertia, friction, and the like.

The dynamic model and a set of input data are used to predict or controlthe performance of drive 66. Input data includes the pattern ofexcitation, control strategy and rotor 24 position information. In anactual drive system, the phase currents are available for measurementand, hence, the position information of rotor 24 can be estimated usinginverse transformation.

Torque in SR motor 20 is developed by the tendency of the magneticcircuit to adopt the minimum reluctance configuration and, hence,unidirectional currents can be used for excitation. The torque in termsof co-energy relations is given by:

$\begin{matrix}{{T_{e}\left( {i,\theta} \right)} = \frac{\partial{W^{\prime}\left( {i,\theta} \right)}}{\partial\theta}} & (1)\end{matrix}$where i is the current in active phase 26, θ is the position angle ofrotor 24, and W′ is the co-energy. If it is assumed that the magneticcircuit is linear, the torque equation becomes

$\begin{matrix}{T_{e} = {\frac{1}{2}i^{2}\frac{\mathbb{d}L}{\mathbb{d}\theta}}} & (2)\end{matrix}$where L is the self-inductance of stator phase 26 at any angle θ.

The present rotation position sensorless method is used to determinerotor 24 position based on the dynamic model of the motor. In order toimplement the method, a software hysteresis controller is used in whichcontroller 72 regulates the phase currents to be within the hysteresisband. The current in active phase 26 can be sampled in intervals of afew microseconds as permissible by the hardware. The gating pulse forthe corresponding active phase 26 is regulated such that the current online 64 remains within the band.

The principle of operation of the proposed sensorless method can beexplained using the following set of equations. The voltage equation forthe conducting phase 26 is given by:

$\begin{matrix}{v = {{Ri} + \frac{\mathbb{d}\psi}{\mathbb{d}t}}} & (3)\end{matrix}$where ν is the voltage applied across the phase winding, (V), R is thephase resistance (Ω), ψ=L(i, θ)i is the flux linkage (wb-turns), andL(i, θ) is the self-inductance of the phase (H).

The self-inductance of stator phase 26, such as phase “A,” may berepresented by a Fourier series whose coefficients depend on thecurrent, as given by equation (4):

$\begin{matrix}{{L\left( {i,\theta} \right)} = {\sum\limits_{j = 0}^{\infty}\;{{L_{j}(i)}{\cos\left( {{{jN}_{r}\theta} + \varphi} \right)}}}} & (4)\end{matrix}$where N, is the number of rotor poles 30 and L_(j) is a constant basedon measured inductance values. As will be recognized by one of ordinaryskill in the art, any sum of orthogonal functions may be used to modelmagnetic characteristics of switched reluctance machine 20. For jranging between 0 and 2, the Fourier series may be written as:L(i,θ)=L ₀(i)+L₁(i)cos N _(r) θ+L ₂(i)cos 2N _(rθ)  (5)The three coefficients L₀, L₁ and L₂ may be derived as a function of thealigned position inductance, L_(a), the unaligned position inductance,L_(u), and the inductance at the midway from the aligned position,L_(m). This results in equations 6–8 as follows:

$\begin{matrix}{L_{0} = {\frac{1}{2}\left\lbrack {{\frac{1}{2}\left( {L_{a} + L_{u}} \right)} + L_{m}} \right\rbrack}} & (6) \\{L_{1} = {\frac{1}{2}\left( {L_{a} - L_{u}} \right)}} & (7) \\{L_{2} = {\frac{1}{2}\left\lbrack {{\frac{1}{2}\left( {L_{a} + L_{u}} \right)} - L_{m}} \right\rbrack}} & (8)\end{matrix}$

Referring now to FIG. 4 a, a schematic diagram illustrating rotoraligned position is shown. In the aligned position, pole 30 issubstantially across from phase 26. This happens at a phase mechanicalangle of 0°. The aligned position inductance as a function of phasecurrent is shown in equation 9.

$\begin{matrix}{L_{a} = {{L\left( {\theta = 0^{0}} \right)} = {\sum\limits_{n = 0}^{n = k}\;{a_{n}i^{n}}}}} & (9)\end{matrix}$

Referring now to FIG. 4 b, a schematic diagram illustrating rotorposition midway from the aligned position is shown. In the midwayposition, pole 30 is between the aligned and unaligned position. Themidway position exactly between the aligned and unaligned position as afunction of phase current is shown in equation 10.

$\begin{matrix}{L_{m} = {{L\left( {\theta = \frac{\pi}{2N_{r}}} \right)} = {\sum\limits_{n = 0}^{n = k}\;{b_{n}i^{n}}}}} & (10)\end{matrix}$

Referring now to FIG. 4 c, a schematic diagram illustrating rotorunaligned position is shown. In the unaligned position, pole 30 issubstantially between two phases 26. For each phase 26, this occurs whenrotor 24 is positioned such that adjacent poles 30 equally straddlephase 26. The unaligned position inductance is not a function of phasecurrent, as shown in equation 11.

$\begin{matrix}{L_{u} = {L\left( {\theta = \frac{\pi}{N_{r}}} \right)}} & (11)\end{matrix}$

The value k in equations 9 and 10 is a degree of approximation. In thepresent case, k=5 yields a good accuracy. As will be recognized by oneof ordinary skill in the art, many other phase inductances may berepresented by a similar set of equations with proper phase shifts.

In the present invention, it is assumed that all phases 26 haveidentical inductance profiles with proper phase shifts. In case of anyphase abnormality, such as airgap eccentricity, there may be somediscrepancy between inductance profiles which can be readily taken intoaccount by the model.

While evaluating the machine performance, the mutual inductances betweenphases 26 can be neglected. Hence, equation (4) can be expanded into thefollowing form:

$\begin{matrix}{v = {{Ri} + {L\frac{\mathbb{d}i}{\mathbb{d}t}} + {i\;\omega\frac{\mathbb{d}L}{\mathbb{d}\theta}} + {i\frac{\mathbb{d}L}{\mathbb{d}i}\frac{\mathbb{d}i}{\mathbb{d}t}}}} & (12)\end{matrix}$where ω is the rotor angular speed in rad/sec. Note that the saturationterm

$i\frac{\mathbb{d}L}{\mathbb{d}i}\frac{\mathbb{d}i}{\mathbb{d}t}$is typically negligible, and will be discarded in the followingdevelopment. The saturation term may be retained if necessary ordesired.

Substituting equation (5) into equation (12) yields the following:

$\begin{matrix}{{v = {{{{Ri}\left( {L_{0} + {L_{1}\cos\;\theta} + {L_{2}\cos\; 2\theta}} \right)}\frac{\mathbb{d}i}{\mathbb{d}t}} + {{\mathbb{i}}\;{\omega\left( {{{- L_{1}}\sin\;\theta} - {L_{2}\sin\; 2\theta}} \right)}}}}\;} & (13)\end{matrix}$The terms in equation (13) can be rearranged into the following form:

$\begin{matrix}{{{{a\;\cos\;\theta} + {b\;\cos\; 2\theta} + {c\;\sin\;\theta} + {d\;\sin\; 2\;\theta} + e} = 0}{where}{{a = {L_{1}\frac{\mathbb{d}i}{\mathbb{d}t}}};}{{b = {L_{2}\frac{\mathbb{d}i}{\mathbb{d}t}}};}{{c = {L_{1} \times i \times \omega}};}{{d = {L_{2} \times i \times \omega}};}{e = {{- v} + {Ri} + {L_{0}\frac{\mathbb{d}i}{\mathbb{d}t}}}}} & (14)\end{matrix}$

As can be seen, all coefficients in equation (14) may be calculated inreal-time once the active phase current is measured and an estimate ofrotor 24 speed is known. Using these coefficients, equation (14) isnumerically solved to get rotor 24 position information.

In one embodiment of the present invention, the dynamic equationspresented in the previous section are solved using a SIMULINK packagefrom MathWorks in order to simulate the performance of system 60. Asimulation time step of 10 μs is used. Individual phase currents,torques and other mechanical quantities such as rotor 24 speed,position, and the like are available from the simulation results.

For simulating the performance of the sensorless scheme, the simulatedactive phase currents are used. Using the active phase current and anestimate of rotor speed, different coefficients in equation (14) arecomputed. Then, equation (14) is numerically solved to estimate therotor position θ. Since the actual value of rotor 24 position is alsoavailable from simulation, it is easy to compare the estimated andactual values of θ.

In this embodiment, a 300 W, 12 V, 1000 RPM, 8/6, four-phase motor isused for simulation and experiments. In order to check the performanceof the sensorless scheme at different operating points, varioussimulations were performed. At each operating point, the estimated andthe actual rotor angle θ are compared and the results are presentedbelow. Control of the sensorless method may be carried out using avariety of means, including one or more of a microprocessor, discreteelectronic components, custom integrated circuits, programmable logicdevices, and the like. For example, a TMS 3200240 digital signalprocessor (DSP) from Texas Instruments may be used. Controller 72 firstinitializes peripherals, sets current limits for the phases, andimplements the observer computations in real-time. Controller 72 thentracks rotor angles continuously and sends out appropriate gating andsensing pulses depending on the frequency counts.

Referring now to FIGS. 5–10, graphs plotting simulated performance areshown.

In the first set of simulations, a conduction angle of 15° (mech) wasused to prevent overlap between adjacent phases 26. Each phase 26 isturned on at 7.5° (mech) from its unaligned position and turned off at22.5° (mech). Each phase 26 is used for rotor 24 position estimationduring phase 26 conduction interval. The estimated angle of rotor 24 isreset to zero whenever any phase 26 starts conducting and that activephase 26 is used for position estimation for 15° (mech), after which thephase 26 is commutated and next phase 26 is turned on. Thus, estimatedrotor 24 angle obtained through simulation is a triangular function oftime with 15° (mech) amplitude. The phase current reference was set at60 amps.

FIGS. 5–6 show results of running SRM 20 at the slow speed of 90 RPMwhile operating under a load torque of 3 Nm. FIG. 5 a illustrates theactual angle of rotor 24 as plot 80. FIG. 5 b illustrates the estimatedangles for rotor 24 as plot 82. FIG. 6 a illustrates one of the phasecurrents, as plot 84, which can be compared with the estimated angle ofrotor 24, shown as plot 86 in FIG. 6 b.

FIGS. 7–8 show the results obtained for a rotor speed of 1500 RPM and aload torque of 1 Nm. FIG. 7 a illustrates the actual angle of rotor 24as plot 88. FIG. 7 b illustrates the estimated angles for rotor 24 asplot 90. FIG. 8 a illustrates one of the phase currents, as plot 92,which can be compared with the estimated angle of rotor 24, shown asplot 94 in FIG. 8 b.

In the second set of simulations, the conduction angle for each phase 26is set equal to 25° (mech). In this case, there may be more than onephase 26 carrying active current and hence available for positionestimation. However, in the present embodiment, only one of the activephases 26 is used for position estimation. Each phase 26 is used forposition estimation in the interval 7.5°<θ<22.50° (mech) with respect toits unaligned position. In this interval, the sensitivity of inductancevariation is maximum. FIG. 9 a illustrates a phase current waveform inplot 96. FIG. 9 b, in plot 98, illustrates the estimated rotor positionsignal. It is clear from FIGS. 9 a and 9 b that only a portion of theconduction interval of the active phase current is used for positionestimation.

Referring now to FIGS. 1 a and 10 b, results from a transient speed testare shown. In order to test the performance of the sensorless schemeduring transient changes in speed, the speed command was changed from 60rad/sec to approximately 10 rad/sec. FIG. 10 a illustrates the actualrotor position in plot 100. FIG. 10 b illustrates the estimated rotorposition in plot 102. It can be seen from FIGS. 10 a and 10 b that thesensorless scheme works well during transients.

The performance of the sensorless scheme was tested in single-pulse modeof operation also, which occurs at speeds above base speed. Thesimulation results showed consistent performance of the sensorlessscheme.

In another embodiment, the experimental setup consists of a 300 W, 12 V,1000 RPM, 8/6, four-phase SRM 20 with a dc generator load. Inverter 66is a two-switch per phase classic converter-type with hysteresis controlemployed to regulate the phase currents at low speeds. Controller 72 isimplemented with a TMS320C30 DSP processor-based microcomputer systemwith a control algorithm developed using assembly language. Formeasuring phase currents, hall effect sensors 74 with high bandwidth areused. Since the position sensorless scheme requires only the phasecurrent measurement, additional hardware is not required. In order tocompare the estimated position signal with the actual position signal, a12-bit resolver is also mounted on driveshaft 62.

Referring now to FIG. 11, a flow diagram of controller operationaccording to an embodiment of the present invention is shown. As will beappreciated by one of ordinary skill in the art, the operationsillustrated in the flow diagram are not necessarily sequentialoperations. The order of steps may be modified within the spirit andscope of the present invention. Also, the method illustrated may beimplemented by any combination of hardware, software, firmware, and thelike. The present invention transcends any particular implementation andthe embodiment is shown in sequential flow chart form for ease ofillustration.

Initialization and startup operations are performed in block 110. Duringstarting, each phase 26 is excited in a sequence with a narrow voltagepulse and the amplitude of the resulting current is measured. Since thespeed induced voltage term is zero, the rate of rise of current dependson the self-inductances of the phases 26. Thus, by probing all fourphases 26 in a sequence, unique value of rotor 24 position can bedetermined.

Active phase current and voltage is sampled in block 112. When motor 20is running at constant speed, controller 72 measures the active phasecurrent and voltage. The voltage across the active phase 26 will bepositive if the switches are “ON” or negative if phase 26 isfree-wheeling through the diodes in drive 66. In an alternativeembodiment where the phase voltage is constant, only the phase currentis measured.

Current limiting is performed in block 114. A check is made for upperand lower current limits in active phase 26 in order to perform softwarehysteresis.

The active phase inductance profile is computed in block 116.Integrating the active phase voltage yields the flux linkage. Dividingthe flux linkage by the active phase current then yields the activephase inductance.

The inductance coefficients are computed in block 118. The inductancecoefficients are computed from the active phase current amplitude andactive phase inductance. This yields, for example, coefficients a, b, c,d and e from equation (14).

The model is solved for the rotor angle in block 120. Equation (14) issolved numerically to get the value of the rotor angle, θ. For solvingequation (14) numerically, a method of bisection is used since the rangeof θ is precisely know. For example, if the phase inductance isrepresented by equation (5), then the range of θ is given by:225°≦θ≦315° (elect) or 7.5°≦θ≦22.5° (mech)  (16)The main advantage of using a method of bisection is that the algorithmconverges very fast and requires only few iterations.

The phase to be excited as well as commutation timing is determined inblock 122. Once the rotor position is known, the controller 72 commandsdrive 66 to switch the appropriate phase 26 at the appropriate time.

The accuracy of the position estimation generally depends on theaccuracy of modeling the SRM and the accuracy with which the activephase currents are measured. The modeling error is not very significantsince the static characteristics obtained through the inductance modeland experiments match well.

For measuring the active phase currents, hall effect sensors are usedwhich have an accuracy of ±1%. However, inverter switching noise shouldbe considered while measuring the active phase current as this mightimpair the accuracy of position estimation.

The resolution of the sensorless scheme generally depends on the rate ofsampling the active phase currents. For simulation purposes a samplingrate of 100 KHz is assumed which results in a resolution of 0.06°(mech). The sampling interval is chosen based on the amount of time thecontroller takes to sample current, compute the various coefficients inequation (14) and then numerically solve equation (14) to obtain therotor angle, θ. Since the processor clock rate is very high and it takesonly one clock cycle which is 50 ns to execute almost all theinstructions, 10 μs sampling time is found to be sufficient.

Since the set of dynamic equations hold good for all the speed ranges,it is possible to use the sensorless scheme practically at all speeds,from standstill to several times the base speed.

Accordingly, a new model based sensorless scheme for SRM drives isprovided. A major advantage of this method is that it requires onlyactive phase terminal measurements and does not require externalhardware.

While embodiments of the invention have been illustrated and described,it is not intended that these embodiments illustrate and describe allpossible forms of the invention. Rather, the words used in thespecification are words of description rather than limitation, and it isunderstood that various changes may be made without departing from thespirit and scope of the invention.

1. A method of controlling a multiphase switched reluctance machinecomprising: measuring the self-inductance of each phase of a pluralityof stator phases, the self-inductance of each phase measured at aplurality of points in a phase rotation, the plurality of phasescomprising at least one active phase, the self-inductance measured forthe at least one active phase comprising a plurality of self-inductancesfor each active phase; constructing a mathematical model of inductancefor each phase based on the measured points, the mathematical modelrepresenting dynamic magnetic machine characteristics, the mathematicalmodel relating phase voltage to phase rotation angle through phaseself-inductance, the mathematical model comprising phase inductance forthe at least one active phase; measuring the phase current of the atleast one active phase of the machine while the machine is in operation;determining the phase rotation angle based on the measured phase currentand the mathematical model for the at least one measured active phase;and controlling the machine based on the determined phase rotationangle.
 2. A method of controlling a multiphase switched reluctancemachine as in claim 1 wherein the mathematical model comprises a sum oforthogonal functions.
 3. A method of controlling a multiphase switchedreluctance machine as in claim 1 wherein measuring the self-inductanceof each phase comprises measuring phase self-inductance at an alignedposition and measuring phase self-inductance at an unaligned position.4. A method of controlling a multiphase switched reluctance machine asin claim 3 wherein measuring the self-inductance of each phase furthercomprises measuring phase self-inductance at least one position betweenthe aligned position and the unaligned position.
 5. A method ofmeasuring the rotational position of a switched reluctance machinerotor, the method comprising: generating a mathematical model based oninductance values measured for each of at least one active phase of aplurality of stator phases, the measured inductance values comprising aplurality of self-inductances for each active phase, the modelrepresenting dynamic magnetic machine characteristics, the mathematicalmodel relating at least one measurable machine parameter with rotorrotational position, the mathematical model comprising phase inductancefor the at least one active phase; measuring the at least one measurablemachine parameter during machine operation; and determining machinerotational position by solving the mathematical model with the at leastone measured machine parameter.
 6. A method of measuring the rotationalposition of a switched reluctance machine rotor as in claim 5 whereinthe mathematical model comprises a sum of orthogonal functions.
 7. Amethod of measuring the rotational position of a switched reluctancemachine rotor as in claim 5 wherein the at least one measurable machineparameter comprises at least one phase self-inductance of the pluralityof self-inductances.
 8. A method of measuring the rotational position ofa switched reluctance machine rotor as in claim 7 wherein the at leastone phase self-inductance comprises phase self-inductance measured at analigned position and phase self-inductance measured at an unalignedposition.
 9. A method of measuring the rotational position of a switchedreluctance machine rotor as in claim 8 wherein the at least one phaseself-inductance further comprises phase self-inductance at least oneposition between the aligned position and the unaligned position.
 10. Aswitched reluctance system comprising: a switched reluctance machinehaving a rotor and a plurality of stator phases, each stator phasehaving a stator phase current; a drive switching each stator phasecurrent; and a controller supplying control signals to the drive, thecontroller receiving at least one sensed machine parameter, thecontroller generating control signals based on a rotor positiondetermined from the at least one sensed machine parameter and from amathematical model based on inductance values measured for at least oneactive phase of the stator phases, the measured inductance valuescomprising a plurality of self-inductances for each active phase, themodel representing dynamic magnetic machine characteristics, themathematical model relating the at least one sensed machine parameterwith rotor position, the mathematical model comprising phase inductancefor the at least one active phase.
 11. A switched reluctance system asin claim 10 wherein the mathematical model comprises a sum of orthogonalfunctions.
 12. A switched reluctance system as in claim 10 whereininductance values measured for the at least one active phase of thestator phases comprise phase self-inductance measured at an alignedposition and phase self-inductance measured at an unaligned position.13. A switched reluctance system as in claim 12 wherein inductancevalues measured for the at least one active phase of the stator phasesfurther comprise phase self-inductance measured at at least one positionbetween the aligned position and the unaligned position.